N. Hungerbuhler

activity

20112025

most citedThe One-Sided Isometric Extension Problem

11 citations · 21 across the 15 of their papers we have counts for

collaborators

20 papers

math.NT2025

Integer triangles with a rational ratio of circumcircle radius to excircle radius

Lorenz Halbeisen, Norbert Hungerbühler, Arman Shamsi Zargar

We consider the problem of finding integer triangles with $R / r$ a positive rational, where $R$ and $r$ are the radii of the circumcircle and an excircle, respectively. We show that…

math.AG2023

Properties of Hesse derivatives of cubic curves

Sayan Dutta, Lorenz Halbeisen, Norbert Hungerbühler

The Hesse curve or Hesse derivative Hess $(Γ_{f})$ of a cubic curve $Γ_{f}$ given by a homogeneous polynomial $f$ is the set of points $P$ such that $det (H_{f} (P)) = 0$ , whe…

math.RA2021★ 2 cited

Polyfunctions over Commutative Rings

Ernst Specker, Norbert Hungerbühler, Micha Wasem

A function $f : R \to R$ , where $R$ is a commutative ring with unit element, is called polyfunction if it admits a polynomial representative $p \in R [x]$ . Based on this notion we intro…

math.AG2021

Reversion Porisms in Conics

Lorenz Halbeisen, Norbert Hungerbühler, Marco Schiltknecht

We give a projective proof of the butterfly porism for cyclic quadrilaterals and present a general reversion porism for polygons with an arbitrary number of vertices on a conic. We…

math.CO2021★ 2 cited

The Ring of Polyfunctions over $Z / n Z$

Ernst Specker, Norbert Hungerbühler, Micha Wasem

We study the ring of polyfunctions over $Z / n Z$ . The ring of polyfunctions over a commutative ring $R$ with unit element is the ring of functions $f : R \to R$ which ad…

math.NT2021

A geometric approach to elliptic curves with torsion groups $Z /10 Z$ , $Z /12 Z$ , $Z /14 Z$ , and $Z /16 Z$

Lorenz Halbeisen, Norbert Hungerbuehler, Maksym Voznyy +1

We give new parametrisations of elliptic curves in Weierstrass normal form $y^{2} = x^{3} + a x^{2} + b x$ with torsion groups $Z /10 Z$ and $Z /12 Z$ over $\math…

math.DG2019★ 1 cited

Equilibria of plane convex bodies

Jonas Allemann, Norbert Hungerbühler, Micha Wasem

We obtain a formula for the number of horizontal equilibria of a planar convex body $K$ with respect to a center of mass $O$ in terms of the winding number of the evolute of $\part…

math.CO2019

Lights Out on graphs

Abraham Berman, Franziska Borer, Norbert Hungerbühler

We model the Lights Out game on general simple graphs in the framework of linear algebra over the field $F_{2}$ . Based upon a version of the Fredholm alternative, we introduc…

math.CO2018

Exotic Steiner Chains in Miquelian Möbius Planes

Norbert Hungerbühler, Gideon Villiger

In the Euclidean plane, two intersecting circles or two circles which are tangent to each other clearly do not carry a finite Steiner chain. However, in this paper we will show tha…

math.NT2018

Congruent number elliptic curves with rank at least two

Lorenz Halbeisen, Norbert Hungerbühler

We give an infinite family of congruent number elliptic curves, each with rank at least two, which are related to integral solutions of $m^{2} = n^{2} + n l + l^{2}$ .

math.HO2018★ 1 cited

Communicating harmonic pencils of lines

Norbert Hungerbühler, Clemens Pohle

Suppose there are $n$ harmonic pencils of lines given in the plane. We are interested in the question whether certain triples of these lines are concurrent or if triples of interse…

math.CO2018★ 1 cited

Resistors in dual networks

Martina Furrer, Norbert Hungerbühler, Simon Jantschgi

Let $G$ be a finite plane multigraph and $G^{'}$ its dual. Each edge $e$ of $G$ is interpreted as a resistor of resistance $R_{e}$ , and the dual edge $e^{'}$ is assigned the dual resistanc…

math.NT2018

A Theorem of Fermat on Congruent Number Curves

Lorenz Halbeisen, Norbert Hungerbühler

A positive integer $A$ is called a congruent number if $A$ is the area of a right-angled triangle with three rational sides. Equivalently, $A$ is a congruent number if and only if…

math.HO2017

An alternative quadratic formula

Norbert Hungerbühler

The classical quadratic formula and some of its lesser known variants for solving the quadratic equation are reviewed. Then, a new formula for the roots of a quadratic polynomial i…

math.CO2015

Steiner's Porism in finite Miquelian Möbius planes

Norbert Hungerbühler, Katharina Kusejko

We investigate Steiner's Porism in finite Miquelian Möbius planes constructed over the pair of finite fields $GF (p^{m})$ and $GF (p^{2 m})$ , for $p$ an odd prime and $m \geq 1$ . Proper…

math.DG2015

Convex Integration and Legendrian Approximation of Curves

Norbert Hungerbühler, Thomas Mettler, Micha Wasem

Using convex integration we give a constructive proof of the well-known fact that every continuous curve in a contact $3$ -manifold can be approximated by a Legendrian curve.

math.DG2014★ 11 cited

The One-Sided Isometric Extension Problem

Norbert Hungerbühler, Micha Wasem

Let $Σ$ be a codimension one submanifold of an $n$ -dimensional Riemannian manifold $M$ , $n ⩾ 2$ . We give a necessary condition for an isometric immersion of $Σ$ into $\mathb…

math.CO2014★ 1 cited

A Poncelet Criterion for special pairs of conics in $P G (2, p)$

Norbert Hungerbühler, Katharina Kusejko

We study Poncelet's Theorem in finite projective coordinate planes over the field $GF (p)$ and concentrate on a particular pencil of conics. For pairs of such conics we investigate…

math.CO2014

Poncelet's Theorem in the four nonisomorphic finite projective planes of order 9

Katharina Kusejko, Norbert Hungerbühler

We study Poncelet's Theorem in the four non-isomorphic finite projective planes of order 9. Among these planes, only the Desarguesian plane turns out to be a Poncelet plane, while…

math.DG2011★ 2 cited

Soliton solutions of the mean curvature flow and minimal hypersurfaces

Norbert Hungerbühler, Thomas Mettler

Let (M,g) be an oriented Riemannian manifold of dimension at least 3 and X a vector field on M. We show that the Monge-Ampère differential system (M.A.S.) for X-pseudosoliton hyper…